lim_(x→0) ((x^n sin^n x)/(x^n −sin^n x)) is non-zero finite, then find n?


Question and Answers Forum

All Questions Topic List
Limits Questions
Previous in All Question Next in All Question
Previous in Limits Next in Limits
Question Number 141965 by gsk2684 last updated on 25/May/21

$\lim_{x \to 0} \frac{x^{n} \sin^{n} x}{x^{n} - \sin^{n} x} i s n o n - z e r o f i n i t e,$ $t h e n f i n d n ?$
Commented by gsk2684 last updated on 25/May/21

$s o l u t i o n p l e a s e$
	Answered by Dwaipayan Shikari last updated on 25/May/21

	$\lim_{x \to 0} s i n x \sim (x - \frac{x^{3}}{3!})$ $\lim_{x \to 0} \frac{x^{n} x^{n}}{x^{n} - {(x - \frac{x^{3}}{6})}^{n}} = \frac{x^{n}}{1 - {(1 - \frac{x^{2}}{6})}^{n}} = \frac{x^{n}}{\frac{{n x}^{2}}{6} + O (x^{4})} = \frac{6}{n} . \frac{x^{n}}{x^{2}}$ $O (x^{4}) \to 0$ $t o g e t a n o n z e r o f i n i t e v a l u e x^{n} = x^{2} t h e n n = 2$
	Commented by gsk2684 last updated on 25/May/21

	$t h a n k y o u$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum